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<div class="title">LMonestep.h</div>  </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2009 Thomas Capricelli &lt;orzel@freehackers.org&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">// This code initially comes from MINPACK whose original authors are:</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// Copyright Jorge More - Argonne National Laboratory</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// Copyright Burt Garbow - Argonne National Laboratory</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment">// Copyright Ken Hillstrom - Argonne National Laboratory</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Minpack license</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="comment">// (a BSD-like license) described in the campaigned CopyrightMINPACK.txt file.</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160; </div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="preprocessor">#ifndef EIGEN_LMONESTEP_H</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="preprocessor">#define EIGEN_LMONESTEP_H</span></div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160; </div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="preprocessor">#include &quot;./InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160; </div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160; </div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> FunctorType&gt;</div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;LevenbergMarquardtSpace::Status</div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;LevenbergMarquardt&lt;FunctorType&gt;::minimizeOneStep(FVectorType  &amp;x)</div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;{</div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;  RealScalar temp, temp1,temp2; </div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;  RealScalar ratio; </div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;  RealScalar pnorm, xnorm, fnorm1, actred, dirder, prered;</div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;  eigen_assert(x.size()==n); <span class="comment">// check the caller is not cheating us</span></div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160; </div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;  temp = 0.0; xnorm = 0.0;</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;  <span class="comment">/* calculate the jacobian matrix. */</span></div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;  <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> df_ret = m_functor.df(x, m_fjac);</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;  <span class="keywordflow">if</span> (df_ret&lt;0)</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;      <span class="keywordflow">return</span> LevenbergMarquardtSpace::UserAsked;</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;  <span class="keywordflow">if</span> (df_ret&gt;0)</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;      <span class="comment">// numerical diff, we evaluated the function df_ret times</span></div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;      m_nfev += df_ret;</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;  <span class="keywordflow">else</span> m_njev++;</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160; </div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;  <span class="comment">/* compute the qr factorization of the jacobian. */</span></div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; x.size(); ++j)</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;    m_wa2(j) = m_fjac.col(j).blueNorm();</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;  QRSolver qrfac(m_fjac);</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;  <span class="keywordflow">if</span>(qrfac.info() != <a class="codeRef" href="../group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a>) {</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;    m_info = <a class="codeRef" href="../group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea1c6e20706575a629b27a105f07f1883b">NumericalIssue</a>;</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;    <span class="keywordflow">return</span> LevenbergMarquardtSpace::ImproperInputParameters;</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;  }</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;  <span class="comment">// Make a copy of the first factor with the associated permutation</span></div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;  m_rfactor = qrfac.matrixR();</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;  m_permutation = (qrfac.colsPermutation());</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160; </div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;  <span class="comment">/* on the first iteration and if external scaling is not used, scale according */</span></div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;  <span class="comment">/* to the norms of the columns of the initial jacobian. */</span></div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;  <span class="keywordflow">if</span> (m_iter == 1) {</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;      <span class="keywordflow">if</span> (!m_useExternalScaling)</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;          <span class="keywordflow">for</span> (<a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> j = 0; j &lt; n; ++j)</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;              m_diag[j] = (m_wa2[j]==0.)? 1. : m_wa2[j];</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160; </div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;      <span class="comment">/* on the first iteration, calculate the norm of the scaled x */</span></div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;      <span class="comment">/* and initialize the step bound m_delta. */</span></div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;      xnorm = m_diag.cwiseProduct(x).stableNorm();</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;      m_delta = m_factor * xnorm;</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;      <span class="keywordflow">if</span> (m_delta == 0.)</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;          m_delta = m_factor;</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;  }</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160; </div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;  <span class="comment">/* form (q transpose)*m_fvec and store the first n components in */</span></div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;  <span class="comment">/* m_qtf. */</span></div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;  m_wa4 = m_fvec;</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;  m_wa4 = qrfac.matrixQ().adjoint() * m_fvec; </div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;  m_qtf = m_wa4.head(n);</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160; </div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;  <span class="comment">/* compute the norm of the scaled gradient. */</span></div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;  m_gnorm = 0.;</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;  <span class="keywordflow">if</span> (m_fnorm != 0.)</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;      <span class="keywordflow">for</span> (<a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> j = 0; j &lt; n; ++j)</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;          <span class="keywordflow">if</span> (m_wa2[m_permutation.indices()[j]] != 0.)</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;              m_gnorm = (std::max)(m_gnorm, <a class="codeRef" href="../namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>( m_rfactor.col(j).head(j+1).dot(m_qtf.head(j+1)/m_fnorm) / m_wa2[m_permutation.indices()[j]]));</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160; </div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;  <span class="comment">/* test for convergence of the gradient norm. */</span></div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;  <span class="keywordflow">if</span> (m_gnorm &lt;= m_gtol) {</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;    m_info = <a class="codeRef" href="../group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a>;</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;    <span class="keywordflow">return</span> LevenbergMarquardtSpace::CosinusTooSmall;</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;  }</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160; </div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;  <span class="comment">/* rescale if necessary. */</span></div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;  <span class="keywordflow">if</span> (!m_useExternalScaling)</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;      m_diag = m_diag.cwiseMax(m_wa2);</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160; </div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;  <span class="keywordflow">do</span> {</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;    <span class="comment">/* determine the levenberg-marquardt parameter. */</span></div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;    internal::lmpar2(qrfac, m_diag, m_qtf, m_delta, m_par, m_wa1);</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160; </div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;    <span class="comment">/* store the direction p and x + p. calculate the norm of p. */</span></div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;    m_wa1 = -m_wa1;</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;    m_wa2 = x + m_wa1;</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;    pnorm = m_diag.cwiseProduct(m_wa1).stableNorm();</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160; </div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;    <span class="comment">/* on the first iteration, adjust the initial step bound. */</span></div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;    <span class="keywordflow">if</span> (m_iter == 1)</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;        m_delta = (std::min)(m_delta,pnorm);</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160; </div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;    <span class="comment">/* evaluate the function at x + p and calculate its norm. */</span></div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;    <span class="keywordflow">if</span> ( m_functor(m_wa2, m_wa4) &lt; 0)</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;        <span class="keywordflow">return</span> LevenbergMarquardtSpace::UserAsked;</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;    ++m_nfev;</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;    fnorm1 = m_wa4.stableNorm();</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160; </div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;    <span class="comment">/* compute the scaled actual reduction. */</span></div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;    actred = -1.;</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;    <span class="keywordflow">if</span> (Scalar(.1) * fnorm1 &lt; m_fnorm)</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;        actred = 1. - numext::abs2(fnorm1 / m_fnorm);</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160; </div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;    <span class="comment">/* compute the scaled predicted reduction and */</span></div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;    <span class="comment">/* the scaled directional derivative. */</span></div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;    m_wa3 = m_rfactor.template triangularView&lt;Upper&gt;() * (m_permutation.inverse() *m_wa1);</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;    temp1 = numext::abs2(m_wa3.stableNorm() / m_fnorm);</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;    temp2 = numext::abs2(<a class="codeRef" href="../namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>(m_par) * pnorm / m_fnorm);</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;    prered = temp1 + temp2 / Scalar(.5);</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;    dirder = -(temp1 + temp2);</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160; </div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;    <span class="comment">/* compute the ratio of the actual to the predicted */</span></div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;    <span class="comment">/* reduction. */</span></div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;    ratio = 0.;</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;    <span class="keywordflow">if</span> (prered != 0.)</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;        ratio = actred / prered;</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160; </div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;    <span class="comment">/* update the step bound. */</span></div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;    <span class="keywordflow">if</span> (ratio &lt;= Scalar(.25)) {</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;        <span class="keywordflow">if</span> (actred &gt;= 0.)</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;            temp = RealScalar(.5);</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;        <span class="keywordflow">if</span> (actred &lt; 0.)</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;            temp = RealScalar(.5) * dirder / (dirder + RealScalar(.5) * actred);</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;        <span class="keywordflow">if</span> (RealScalar(.1) * fnorm1 &gt;= m_fnorm || temp &lt; RealScalar(.1))</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;            temp = Scalar(.1);</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;        <span class="comment">/* Computing MIN */</span></div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;        m_delta = temp * (std::min)(m_delta, pnorm / RealScalar(.1));</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;        m_par /= temp;</div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;    } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (!(m_par != 0. &amp;&amp; ratio &lt; RealScalar(.75))) {</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;        m_delta = pnorm / RealScalar(.5);</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;        m_par = RealScalar(.5) * m_par;</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;    }</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160; </div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;    <span class="comment">/* test for successful iteration. */</span></div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;    <span class="keywordflow">if</span> (ratio &gt;= RealScalar(1e-4)) {</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;        <span class="comment">/* successful iteration. update x, m_fvec, and their norms. */</span></div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;        x = m_wa2;</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;        m_wa2 = m_diag.cwiseProduct(x);</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;        m_fvec = m_wa4;</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;        xnorm = m_wa2.stableNorm();</div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;        m_fnorm = fnorm1;</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;        ++m_iter;</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;    }</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160; </div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;    <span class="comment">/* tests for convergence. */</span></div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;    <span class="keywordflow">if</span> (<a class="codeRef" href="../namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(actred) &lt;= m_ftol &amp;&amp; prered &lt;= m_ftol &amp;&amp; Scalar(.5) * ratio &lt;= 1. &amp;&amp; m_delta &lt;= m_xtol * xnorm)</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;    {</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;       m_info = <a class="codeRef" href="../group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a>;</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;      <span class="keywordflow">return</span> LevenbergMarquardtSpace::RelativeErrorAndReductionTooSmall;</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;    }</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;    <span class="keywordflow">if</span> (<a class="codeRef" href="../namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(actred) &lt;= m_ftol &amp;&amp; prered &lt;= m_ftol &amp;&amp; Scalar(.5) * ratio &lt;= 1.) </div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;    {</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;      m_info = <a class="codeRef" href="../group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a>;</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;      <span class="keywordflow">return</span> LevenbergMarquardtSpace::RelativeReductionTooSmall;</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;    }</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;    <span class="keywordflow">if</span> (m_delta &lt;= m_xtol * xnorm)</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;    {</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;      m_info = <a class="codeRef" href="../group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a>;</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;      <span class="keywordflow">return</span> LevenbergMarquardtSpace::RelativeErrorTooSmall;</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;    }</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160; </div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;    <span class="comment">/* tests for termination and stringent tolerances. */</span></div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;    <span class="keywordflow">if</span> (m_nfev &gt;= m_maxfev) </div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;    {</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;      m_info = <a class="codeRef" href="../group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea6a68dfb88a8336108a30588bdf356c57">NoConvergence</a>;</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;      <span class="keywordflow">return</span> LevenbergMarquardtSpace::TooManyFunctionEvaluation;</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;    }</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;    <span class="keywordflow">if</span> (<a class="codeRef" href="../namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(actred) &lt;= NumTraits&lt;Scalar&gt;::epsilon() &amp;&amp; prered &lt;= NumTraits&lt;Scalar&gt;::epsilon() &amp;&amp; Scalar(.5) * ratio &lt;= 1.)</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;    {</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;      m_info = <a class="codeRef" href="../group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a>;</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;      <span class="keywordflow">return</span> LevenbergMarquardtSpace::FtolTooSmall;</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;    }</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;    <span class="keywordflow">if</span> (m_delta &lt;= NumTraits&lt;Scalar&gt;::epsilon() * xnorm) </div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;    {</div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;      m_info = <a class="codeRef" href="../group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a>;</div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;      <span class="keywordflow">return</span> LevenbergMarquardtSpace::XtolTooSmall;</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;    }</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;    <span class="keywordflow">if</span> (m_gnorm &lt;= NumTraits&lt;Scalar&gt;::epsilon())</div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;    {</div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;      m_info = <a class="codeRef" href="../group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a>;</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;      <span class="keywordflow">return</span> LevenbergMarquardtSpace::GtolTooSmall;</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;    }</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160; </div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;  } <span class="keywordflow">while</span> (ratio &lt; Scalar(1e-4));</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160; </div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;  <span class="keywordflow">return</span> LevenbergMarquardtSpace::Running;</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;}</div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160; </div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;  </div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;} <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160; </div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;<span class="preprocessor">#endif </span><span class="comment">// EIGEN_LMONESTEP_H</span></div>
<div class="ttc" id="agroup__enums_html_gga85fad7b87587764e5cf6b513a9e0ee5ea1c6e20706575a629b27a105f07f1883b"><div class="ttname"><a href="../group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea1c6e20706575a629b27a105f07f1883b">Eigen::NumericalIssue</a></div><div class="ttdeci">NumericalIssue</div></div>
<div class="ttc" id="agroup__enums_html_gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf"><div class="ttname"><a href="../group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Eigen::Success</a></div><div class="ttdeci">Success</div></div>
<div class="ttc" id="agroup__enums_html_gga85fad7b87587764e5cf6b513a9e0ee5ea6a68dfb88a8336108a30588bdf356c57"><div class="ttname"><a href="../group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea6a68dfb88a8336108a30588bdf356c57">Eigen::NoConvergence</a></div><div class="ttdeci">NoConvergence</div></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div></div>
<div class="ttc" id="anamespaceEigen_html_a62e77e0933482dafde8fe197d9a2cfde"><div class="ttname"><a href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a></div><div class="ttdeci">EIGEN_DEFAULT_DENSE_INDEX_TYPE Index</div></div>
<div class="ttc" id="anamespaceEigen_html_ae27242789e7e62a8c42579b79be59b1a"><div class="ttname"><a href="../namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">Eigen::abs</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_abs_op&lt; typename Derived::Scalar &gt;, const Derived &gt; abs(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_af4f536e8ea56702e63088efb3706d1f0"><div class="ttname"><a href="../namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">Eigen::sqrt</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_sqrt_op&lt; typename Derived::Scalar &gt;, const Derived &gt; sqrt(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
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